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二阶矩限制下的Hajek-Renyi型不等式及其应用 被引量:12

HAJEK-RENYI-TYPE INEQUALITY UNDER SECOND MOMENT CONDITIONS AND ITS APPLICATION
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摘要 在二阶矩限制下,获得了Hajek-Renyi型不等式,并给出了结果在PA,NA,Lr-混合序列场合下的应用.推广了Prakasa Rao关于PA序列的结果. In this paper, we obtain the Hajek-Renyi type inequality under second mement conditions, some applications for the PA, NA sequences and the Lr-mixingale sequences are given. It generalizes the Prakasa Rao's results for positively associated sequences.
出处 《应用数学学报》 CSCD 北大核心 2005年第2期227-235,共9页 Acta Mathematicae Applicatae Sinica
基金 国家自然科学基金(10271001号)资助项目.
关键词 二阶矩 限制 混合序列 不等式 PA Hajek-Renyi型不等式 Hajek-Renyi type inequality, almost sure convergence, positively associated sequences, negatively associated sequences, Lr-mixingale sequences
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参考文献6

  • 1Hajek J, Renyi A. A Generalization of an Inequality of Kolomogorov. Acta Math. Acad. Sci. Hungar,1955, 6:281-284
  • 2Prakasa Rao. Hajek-Renyi-type Inequality for Associated Sequences. Satist. Probab. Lett., 2002, 57:139-143.
  • 3Newman C M., Wright A L. An Invariance Principle for Certain Dependent Sequences. Ann. Probab.,1981, 9(4): 671-675.
  • 4Shao Q M. A Comparison Theorem on Moment Inequalities Between Negatively Associated and Independent Random Variables. J. Theore. Probab., 2000, 13(2): 343-356.
  • 5Loeve M. Probability Theory I, 4th Edition. New York, Heidelberg, Berlin: Springer-Verlag, 1977.
  • 6Shuhe Hu. Some New Results for the Strong Law of Large Numbers. Acta Mathematica Sinica.,2003, 46(6): 1123-1134 (in Chinese).

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